Unit 11 23 HMM Localization Example.mp4 knowitvideos English Japanese

Unit 11 23 HMM Localization Example.mp4YouTube↗ IA↗(long shot)
Film & Animation 6.8K views 36 likes 2 dislikes 14 Nov 2011

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[Thrun] Here is the application of HMM to a real robot localization example.

これは実際のロボットの現在地測定問題に HMMを適用した例です

This robot is in a world that's 1-dimensional and it is lost.

このロボットは一次元の世界にいて自分の場所を見失いました

It has initial uncertainty about where it is,

どこにいるかを知りません

and it is actually located next to a door but it doesn't know.

実際にはドア側にいますがそれを知りません

It's also given a map of the world, and the distribution of all possible states, here noted as s, is given by this histogram.

ロボットはこの世界の地図を持っておりすべての取りうる状態sは

We bin the world into small bins, and for each bin we assign a single numerical probability of the robot being there.

ヒストグラムとして与えられますこの世界を小さく分割してそれぞれにロボットがいる確率を割り当てます

The fact they have all the same height means that the robot is maximally uncertain as to where it is.

すべての高さが等しいということはロボットの位置が全然分からないということです

Let's assume this robot is going to sense and it senses to be next to a door.

ロボットが検知して扉側にいると分かったとしましょう

The red graph over here is the probability of seeing a door

この赤いグラフはこの環境でそれぞれの場所について

for different locations in the environment.

扉を見つける可能性を表しています

There are 3 different doors, and seeing a door is more likely here than it is in between.

3つの扉がありここでは中間よりも扉を見つける可能性が高いです

It might still see a door here, but it's just less likely.

ここでも扉を見つけられますが可能性は高くはありません

We now apply Bayes rule.

ここでベイズの定理を適用します

We multiply the prior with this measurement probability to obtain the posterior.

事後確率を求めるためこの出力の確率に事前確率を掛けます

That was our measurement update. It's that simple.

これが出力値の更新です　単純ですね

So you can see how all these uniform values over here become nonuniform values over here

すべて等しい値がこの曲線を掛けることで

multiplied by this curve over here.

不均一な値に変わったのが分かります

The story progresses by the robot taking an action to the right,

ロボットが右に進んで今度は次の状態を予測します

and this is now the next state prediction part, the what we call convolution part

私たちはこれを畳み込みまたは状態遷移と呼んでいます

or state transition part, where these little bumps over here get shifted along with the robot

ここで小さな山はロボットと一緒に移動し少し平らになります

and they are flattened out a little bit just because robot motion has used uncertainty.

ロボットの移動は不確実なものとして扱われるからです

Again, it's a really simple operation.

これも単純な操作ですね

You shift those to the right and you smooth them out a little bit

これらを右に移動させ全体を少しスムーズにします

to account for the control noise in the robot's actuators.

ロボットの移動機器の制御によるノイズを考慮するためです

And now we get to the point that the robot senses again, and this robot senses a door again.

再びロボットがセンサを作動させる場所へたどり着き扉を認識します

And see what happens. It multiplies.

何が起こるでしょうか　乗算してみましょう

It's now a nonuniform prior over here with the same measurement probability as before,

今の事前確率は平坦ではなく出力の確率は以前と同じです

but now we get a distribution that's peaked over here and has smaller bumps at various other places,

しかし今度はここに山ができ小さな山が複数ある確率分布になりました

the reason being the only place where my prior has a higher probability

事前確率が高く出力の確率も高かった唯一の場所が

and my measurement probability is also high probability is the second door,

2つ目の扉であったため

and as a result of our distribution over here, it assumes a much larger value.

結果的により大きな値を記録しています

If you look at that picture, that is really easy to implement,

この図を見ると実装はとても簡単で

and that's what we did all along when we talked about rain and sun and so on.

天気の例などで行った事と同じだと分かります

It's really a very simple algorithm.

とても単純なアルゴリズムです

Measurements are multiplications, and motion become essentially convolutions

観測は乗算であり動作はシフトに

which are shifts with added noise.

ノイズを加味したものになります

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